3.11 Solving Quadratic Relations

Case 1: Solving quadratic equations with no linear term.
Method: isolate the quadratic term and solve.

Case 2: Solving quadratic equations with a linear term.
Method: rearrange the equation so one side equals 0.
factor and solve.

Note that "finding the roots " means finding the zeros

HW:
p. 315 # 2agik, 3, 6de, 13, 17

3.12 Sample Problems.



A fifth problem type is where you are given an object like a bridge. You can create two zeros by placing a sketch on the x-axis, and you are given another point. From this you can find the equation that models the bridge and find the vertex.

A sixth type of problem uses the Pythagorean theorem.

UNIT TEST Wednesday April 28th,
Vocabulary - roots, zeroes, parabola, quadratic, monic, complex, perfect square, difference of squares.

- second differences, know how to calculate and whether the graph opens up or down.

- Given Factored Form
  • find zeros
  • find equation of axis of symmetry
  • find vertex
  • draw an reasonably accurate graph
  • use FOIL to expand into standard form
  • find y-intercept (by expanding and using c as y-intercept)
  • find 'a' and know how it affects the direction of opening

Given a graph
  • finding the roots, vertex and axis of symmetry from a graph of a parabola

Given standard form
  • convert to factored form by factoring.

Solving quadratic relations to problem solve.
See the five types of problems in

Skills needed
  • finding zeros (roots)
  • finding midpoint
  • expanding
  • factoring (common, monic and complex)